Upon investigation, it looks like the two are indeed tripping over each other. The Google Sitemaps includes admin_functions.php because it needs the get_home_path() function provided in it, but the WP-ShortStat plugin specifically will not log the hit if admin_functions.php is loaded to avoid logging the admin pages (makes sense, I guess).
Since it seems that I would never be publishing, editing or deleting a post without being in the admin interface, I think it’s safe to disable the inclusion in the Google Sitemaps plugin.
To do that, open Google Sitemaps 2.7 sitemap.php file and scroll down to line 159. Change it from:
require_once(ABSPATH . 'wp-admin/admin-functions.php');
to
// require_once(ABSPATH . 'wp-admin/admin-functions.php');
save it and re-upload it.
So far so good on my site ??
–Steve